An actuator of this kind is described in German Published Patent Application No. 198 26 047. When the gas exchange valves on the exhaust side of a cylinder of the internal combustion engine are still in the closed position at the beginning of the discharge stroke, they must work against a high internal cylinder pressure counteracting the hydraulic opening force. The internal cylinder pressure is high only when the gas exchange valves are in the closed state, however, whereas it drops rapidly after they open. A relatively high hydraulic opening pressure is consequently necessary only at the beginning of the opening phase, whereas a smaller opening force is sufficient once opening has already occurred and enlarged the flow cross section. The known actuator, however, always makes an opening force of identical magnitude available at the exhaust-side gas exchange valves, regardless of the particular requirement.